The engine, trans and cooling system would be my main concerns. I used to own a Cruze also made in Korea that also had a small turbo 4cyl, which is same engine/trans used in the Sonic.
We had GM buy back our Cruze under the lemon law. Within 60k miles this car was it in the shop for warranty work 10 times and under the lemon law any single problem that isn't fixed within 3 visits qualifies it to be bought back by the manufacturer. In our case it was the transmission that failed 3 times. Basically the car would randomly downshift into 1st gear when travelling over 60 mph with or without cruise control engaged. This problem nearly killed me and my family on 2 different occasions. Imagine cruising down the freeway and your car suddenly slams into 1st gear, then you completely lose traction going into an uncontrolled skid with other cars trying to react around you. The dealership never found the problem. They tried new programming, new trans control modules, etc, but nothing worked, so that was it for us. The engine never gave us problems except for an intake manifold gasket. The battery cracked open and spilled acid all over the main wiring harness. The cooling system developed 3 separate leaks mainly due to housings, pipes and other parts being made of plastic instead of good old aluminum. Since this car was made in Korea like the Trailblazer I'm of course a little concerned, but it doesn't mean anything bad will ever happen, fingers crossed, lol. I can say for sure this SUV is far nicer in evey way than the Cruze or the Corolla we traded in for it.
Steve